Non-contact optical methods for performing surface profile measurements have been extensively studied, particularly in light of their importance in fields, such as automated manufacturing, component quality control, medicine, robotics, and solid modeling applications. Optical techniques are most promising for non-contact, high-speed, and high-accuracy surface profiling. In such techniques, a one-dimensional periodic pattern or grating image is projected onto a surface under test. The image of the pattern is observed from another direction and that image is deformed by the surface. The deformed periodic pattern or grating image is captured and analyzed to determine the surface profile.
Different techniques have been developed to analyze the deformed pattern image. For instance, an optical Moire technique uses a reference pattern that has no deformation to correlate with the deformed pattern and to generate a surface contour mapping. See D. M. Meadows, W. O. Johnson, and J. B. Allen, Applied Optics, 9, 942, (1970), H. Takasaki, Applied Optics, 9, 1467, (1970), P. Benoit, E. Mathieu, J. Hormiere and A. Thomas, Nouv. Rev. Optics 6, 67 (1975); and T. Yatagai, M. Idesawa, and R. saito, Proc. Photo-Opt. Instrum. Eng. 361, 81 (1982)). The Moire technique requires complicated fringe analysis software to obtain a quantitative surface profile and has a low measurement accuracy. A phase modulation technique was developed to improve the measurement accuracy and to achieve automation for the Moire technique. See G. Indebetouw, Applied Optics, 18, 91, (1979).
An alternative approach to the Moire technique is to directly analyze the deformed grating image. One method is to find the fringe centers, and then to perform two-dimensional (2-D) data interpolation. This approach requires complex computation and is low in accuracy. Another approach is to perform fast Fourier transformation (FFT) of the deformed pattern. See M. Takeda, and K. Mutoh, Applied Optics, 22, 3977 (1983). However, any method based on the analysis of distorted pattern images suffers from image noise and has limited measurement capabilities.
Phase shift measurement techniques are well-known concepts developed in optical interferometry. In order to precisely determine the phase at each point on an interference pattern, a temporal sinusoidal intensity variation is generated by shifting the relative phase between two interference beams. Instead of using only one interference pattern, the technique takes N (where N&gt;2) interference patterns. Prior to taking each image, a phase shift of one N.sup.th of the wavelength is introduced between two interference beams. From the N interference patterns, the phase at each point on the interference pattern can be precisely calculated. The technique has been widely used in precision optical testing.
In order to extend the above temporal phase shift concept for analyzing the deformed grating in space domain, U.S. Pat. No. 4,641,972 to M. Halioua ("the Halioua patent") proposed to use a spatial sinusoidal grating to simulate temporal sinusoidal intensity variation. The Halioua patent has extended the temporal phase shift measurement technique for measurements of the phases of the deformed spatial sinusoidal pattern. The Halioua patent suggests two possible approaches to generate a sinusoidal fringe pattern. The first approach is to use a laser to generate interference fringes, and the second approach is to project an image of a sinusoidal grating.
The first approach has two problems. The first problem is that the generated interference pattern is extremely vulnerable to air turbulence, vibration, and defects in the optical components. For example, when using Michelson, Mach-Zehnder or optical fiber interferometers, tiny air turbulences or vibrations result in large measurement errors and a significantly large error magnification. The error magnification is equal to the ratio between the grating period and the optical wavelength. Assuming that the fringe period is 1 mm and the optical wavelength is 0.5 .mu.m (i.e., green light), the error magnification is about 2000. If a common path interferometer is used, such as a shearing polarization interferometer (which is employed in the Halioua patent), the crystal nonuniformity in a Wollaston prism causes fringe deformation and thus phase measurement errors. The accuracy of the quarter waveplate and the non-uniformity of the rotating polarizer also cause phase measurement errors.
The second problem associated with the laser-generated sinusoidal interference pattern is laser speckle noise. Laser coherent noise significantly deteriorates the measurement accuracy and reduces the overall precision of the profiling technique.
The second approach for generating a sinusoidal pattern is to project an image of a sinusoidal grating onto a surface under testing. The problem with the second approach is that a sinusoidal grating with high contrast and accurate waveform is very difficult to generate. Commercially available sinusoidal gratings have poor contrast and result in a poor measurement signal to noise ratio. Thus, the two approaches proposed in the Halioua patent for generating sinusoidal patterns are impractical for precise surface profilometry.
There is a need to provide an improved method and apparatus for obtaining high precision measurements to profile a surface of an object and, more specifically, to profile a gear surface.
Accordingly, it is an object of the present invention to provide an improved high precision surface profiling system to precisely determine the macroscopic absolute surface profile of an object.
It is a further object of the present invention to provide a high precision surface profiling system to precisely determine the macroscopic absolute surface profile of a gear surface.
Another object of the present invention is to provide a surface profiling system which provides the flexibility of employing different types of grating images or intensity patterns.
It is another object of the present invention to provide a compact optical head arrangement for projecting an intensity pattern onto a surface under test.
It is also an object of the present invention to provide an improved method and apparatus for calibrating a surface profiling system, without the need for physical master gears.
Another object of the present invention is to provide a surface profiling system, with reduced phase measurement error.
It is a further object of the present invention to provide a method and apparatus for dynamic reflectivity compensation of a projection and imaging system of a surface profiling system.